Based on the truncated Dyson-Schwinger equations for the fermion propagator with N fermion flavors at zero temperature, the chiral phase transition of quantum electrodynamics in 2 + 1 dimensions (QED(3)) with boson mass-which is obtained via the Anderson-Higgs mechanism-is investigated. In the chiral limit, we find that the critical behavior of QED(3) with a massless boson is different from that with a massive boson: the chiral phase transition in the presence of a nonzero boson mass reveals the typical second-order phase transition, at either the critical boson mass or a critical number of fermion flavors, while for a vanishing boson mass it exhibits a higher than second-order phase transition at the critical number of fermion flavors. Furthermore, it is shown that the system undergoes a crossover behavior from a small number of fermion flavors or boson mass to its larger one beyond the chiral limit.